Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-Find $\sin \theta$, given that $\cos \theta = \frac { 2 } { 7 }$ and $\theta$ is in quadrant IV.
A) $- 3 \sqrt { 5 }$
B) $- \frac { 7 } { 2 }$
C) $- \frac { 3 \sqrt { 5 } } { 2 }$
D) $- \frac { 3 \sqrt { 5 } } { 7 }$

Question

Quizplus · Accepted Answer

In the fourth quadrant, sine is negative, and using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, we find $\sin \theta = -\sqrt{1 - \cos^2 \theta} = -\sqrt{1 - \left(\frac{2}{7}\right)^2} = -\frac{3\sqrt{5}}{7}$.

Convert the Angle to Decimal Degrees and Round to the Nearest